1. So chronologically "yunoshetskyi rozriad" is before "sportivnyi"?
Like: Young figurist -> 3rd child -> 2nd child -> 1st child -> 2nd sports -> 1st sports -> KMC -> MC ?
Yes.
To pretend to child grade skater must successfully perform test for "young figurist". This test includes 3 jumps - 0,5 turn Axel and two differenf 1 turn jumps, one spin on base level, one ChSq.
Young figurist is given by tests, all higher - by competitions. 1st sports grade and lower - by score (and must meet the requrements, for example in FS for 1st sports grade - 2A and combo with 2A, 4 or more different double and triple jumps, all elements for GOE -1 or higher).
KMS and higher - by place (for example KMS - place 1-10 at JrNats or 1-3 at Event of Russian Cup etc., and meet the requrements too).
Two highest titles - MSMK and ZMS (Honored Master of Sports) need only places at Internationals, no requrements.
MSMK - place 7 or higher at Worlds, 6 or higher at Euro etc.
ZMS - medal of Olympics
or gold medal of Worlds
or to win GPF or Euro and have 150 scoring points which are given for medals of Euro, Worlds and GPF.
Skaters may omit some grades. I know girl who newer had 2nd sports grade, she got 1st sports grade after 1st childs grade.
But highest grades and titles (KMS and higher) are given only in order. Radionova was KMS when won JrWorls-2013, and there were two orders of Minister of Sports of the same day - MS and MSMK for her.
2. Is there no 3rd sports grade?
There
is 3rd sports grade.
Programs are the same as 2nd sports grade.
For 2nd sports grade is needed total score 65 for boys and 60 for girls or higher, if requirements are met but score is lower - 3rd grade.
3. What are the age limits in 1-3 childs grade?
4. How can I get to know what grade certain skater is? Fskate.ru provides only names.
3 and 4 - I don't know.